TY - JOUR

T1 - Uniformly Discrete Forests with Poor Visibility

AU - Alon, Noga

N1 - Funding Information:
† Research supported in part by USA–Israeli BSF grant 2012/107, by ISF grant 620/13, by the Israeli I-Core programme and by the Fund for Mathematics.
Funding Information:
I thank Yaar Solomon for helpful discussions, comments and references, and Gady Kozma for fruitful suggestions and discussions. Research supported in part by USA-Israeli BSF grant 2012/107, by ISF grant 620/13, by the Israeli I-Core programme and by the Fund for Mathematics.
Publisher Copyright:
© 2017 Cambridge University Press.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ-1-o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlierestimates of Peres, of Solomon and Weiss, and of Adiceam.

AB - We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive ϵ < 1, and every line segment in the plane of length at least ϵ-1-o(1), there is a point of F within distance ϵ of the segment. This is tight up to the o(1)-term in the exponent, improving earlierestimates of Peres, of Solomon and Weiss, and of Adiceam.

UR - http://www.scopus.com/inward/record.url?scp=85030864065&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030864065&partnerID=8YFLogxK

U2 - 10.1017/S0963548317000505

DO - 10.1017/S0963548317000505

M3 - Article

AN - SCOPUS:85030864065

SN - 0963-5483

VL - 27

SP - 442

EP - 448

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 4

ER -